I'm not a biologist, however I can perhaps offer some reasoning.
Chromosomes carry genes in very compact, and complex strands of
proteins that attach and connect along the double-helix DNA form.
Genes are blueprint markers that identify, and instruct the
development and characterists of each individual. DNA is the amalgum
of these things along with other enzhymes, proteins, acids, and
hormones that form double-helix strands.
I hope this makes sense and can help.

From: http://www.doctorcarlos.com/newhtml/genomeexplain.html
Introduction
The complete set of instructions for making an organism is called its
genome. It contains the master blueprint for all cellular structures
and activities for the lifetime of the cell or organism. Found in
every nucleus of a persons many trillions of cells, the human genome
consists of tightly coiled threads of deoxyribonucleic acid (DNA) and
associated protein molecules, organized into structures called
chromosomes.
If unwound and tied together, the strands of DNA would stretch more
than 5 feet but would be only 50 trillionths of an inch wide. For each
organism, the components of these slender threads encode all the
information necessary for building and maintaining life, from simple
bacteria to remarkably complex human beings. Understanding how DNA
performs this function requires some knowledge of its structure and
organization.
DNA
In humans, as in other higher organisms, a DNA molecule consists of
two strands that wrap around each other to resemble a twisted ladder
whose sides, made of sugar and phosphate molecules, are connected by
rungs of nitrogen- containing chemicals called bases. Each strand is a
linear arrangement of repeating similar units called nucleotides,
which are each composed of one sugar, one phosphate, and a nitrogenous
base (Fig. 2: DNA Structure). Four different bases are present in DNA:
adenine (A), thymine (T), cytosine (C), and guanine (G). The
particular order of the bases arranged along the sugar- phosphate
backbone is called the DNA sequence; the sequence specifies the exact
genetic instructions required to create a particular organism with its
own unique traits.
The two DNA strands are held together by weak bonds between the bases
on each strand, forming base pairs (bp). Genome size is usually stated
as the total number of base pairs; the human genome contains roughly 3
billion bp
Each time a cell divides into two daughter cells, its full genome is
duplicated; for humans and other complex organisms, this duplication
occurs in the nucleus. During cell division the DNA molecule unwinds
and the weak bonds between the base pairs break, allowing the strands
to separate. Each strand directs the synthesis of a complementary new
strand, with free nucleotides matching up with their complementary
bases on each of the separated strands. Strict base- pairing rules are
adhered to adenine will pair only with thymine (an A- T pair) and
cytosine with guanine (a C- G pair). Each daughter cell receives one
old and one new DNA strand. The cells adherence to these base- pairing
rules ensures that the new strand is an exact copy of the old one.
This minimizes the incidence of errors (mutations) that may greatly
affect the resulting organism or its offspring.
Genes
Each DNA molecule contains many genes the basic physical and
functional units of heredity. A gene is a specific sequence of
nucleotide bases, whose sequences carry the information required for
constructing proteins, which provide the structural components of
cells and tissues as well as enzymes for essential biochemical
reactions. The human genome is estimated to comprise more than 30,000
genes.
Human genes vary widely in length, often extending over thousands of
bases, but only about 10% of the genome is known to include the
protein- coding sequences (exons) of genes. Interspersed within many
genes are intron sequences, which have no coding function. The balance
of the genome is thought to consist of other noncoding regions (such
as control sequences and intergenic regions), whose functions are
obscure. All living organisms are composed largely of proteins; humans
can synthesize at least 100,000 different kinds. Proteins are large,
complex molecules made up of long chains of subunits called amino
acids. Twenty different kinds of amino acids are usually found in
proteins. Within the gene, each specific sequence of three DNA bases
(codons) directs the cells protein- synthesizing machinery to add
specific amino acids. For example, the base sequence ATG codes for the
amino acid methionine. Since 3 bases code for 1 amino acid, the
protein coded by an average- sized gene (3000 bp) will contain 1000
amino acids. The genetic code is thus a series of codons that specify
which amino acids are required to make up specific proteins.
The protein- coding instructions from the genes are transmitted
indirectly through messenger ribonucleic acid (mRNA), a transient
intermediary molecule similar to a single strand of DNA. For the
information within a gene to be expressed, a complementary RNA strand
is produced (a process called transcription) from the DNA template in
the nucleus. This mRNA is moved from the nucleus to the cellular
cytoplasm, where it serves as the template for protein synthesis. The
cells protein- synthesizing machinery then translates the codons into
a string of amino acids that will constitute the protein molecule for
which it codes. In the laboratory, the mRNA molecule can be isolated
and used as a template to synthesize a complementary DNA (cDNA)
strand, which can then be used to locate the corresponding genes on a
chromosome map. The utility of this strategy is described in the
section on physical mapping.
Chromosomes
The 3 billion bp in the human genome are organized into 24 distinct,
physically separate microscopic units called chromosomes. All genes
are arranged linearly along the chromosomes. The nucleus of most human
cells contains 2 sets of chromosomes, 1 set given by each parent. Each
set has 23 single chromosomes22 autosomes and an X or Y sex
chromosome. (A normal female will have a pair of X chromosomes; a male
will have an X and Y pair.) Chromosomes contain roughly equal parts of
protein and DNA; chromosomal DNA contains an average of 150 million
bases. DNA molecules are among the largest molecules now known.
Chromosomes can be seen under a light microscope and, when stained
with certain dyes, reveal a pattern of light and dark bands reflecting
regional variations in the amounts of A and T vs G and C. Differences
in size and banding pattern allow the 24 chromosomes to be
distinguished from each other, an analysis called a karyotype. A few
types of major chromosomal abnormalities, including missing or extra
copies of a chromosome or gross breaks and rejoinings
(translocations), can be detected by microscopic examination; Downs
syndrome, in which an individual's cells contain a third copy of
chromosome 21, is diagnosed by karyotype analysis (Fig. 6: Karyotype).
Most changes in DNA, however, are too subtle to be detected by this
technique and require molecular analysis. These subtle DNA
abnormalities (mutations) are responsible for many inherited diseases
such as cystic fibrosis and sickle cell anemia or may predispose an
individual to cancer, major psychiatric illnesses, and other complex
diseases.
-d

DNA is the material that Genes are made of. It contains a code in its
sequence of units which are called Nucleotides.
A Gene is a particular sequence of Nucleotides along the DNA strand
that codes for the production of a single end - product (either a
protein or part of a protein called a polypeptide).
Chromosomes are complex structures which include other substances but
ultimately have the DNA (and hence the Genes), wound up in a
supercoiled manner.
So, Chromosomes are based on DNA in ordered sequences; The sequences
represent Genes and DNA is the Genetic Material.

I'm going to lay it out plain, from the point of view of a working
molecular biologist.
A gene is a template used for making a protein PLUS the instructions
and "handles" for turning that template on and off. That is what it
is. Physically, for most organisms, these genes are made of DNA.
I'll use animals/humans as a model for the rest of what I write.
Plants have some differences, and bacteria more, but the principles
are fairly the same.
The "core bit" of a gene is the "coding sequence" (CDS). This is that
part of the gene that actually is the template for the protein. The
CDS is very often not all in one piece. Instead, it is split up into
"exons" that have other stretches of DNA (called "introns") in
between. Thes "introns" often have specific sequences on them that
will bind to proteins that are used to control the gene. They are NOT
"junk DNA". There is no such thing as "junk DNA", only DNA that we do
not yet understand. In addition to the exons and introns, there are
two more important parts of the gene. The length of DNA that is
before the beginning of the CDS has two subsections, the "promoter"
and the "5'-UTR". The promoter usually has the most sequences that
are bound by control proteins, and it usually is the part of the gene
that most controls when or if the the protein is expressed, and how
much. The 5'-UTR is transcribed as part of the RNA used for the final
steps of producing a primary protein strand but does not serve as a
template for the protein. It very often involved in further control
and fine-tuning of the timing and amount of a protein. The final
important segment of a gene also has two parts, called a "terminator"
and a "3'-UTR". The terminator ensures that the cell stops
transcribing DNA to RNA at the end of the gene. The 3'-UTR is very
often important in making sure that RNA stays stable as long as it is
needed.
All of these above segments are DNA, all in a single segment of double
helix, all one gene. Many genes then exist end-to-end (or even
overlapping!), all on a single very large piece of double-helix DNA.
This very large piece has specific DNA sequences that do not act to
control genes nor act as a protein template. These specific stretches
of DNA exist to provide locations for specific proteins to bind to.
The proteins form a "scaffold". The very long piece of DNA, with many
genes upon it and the scaffold-binding DNA, plus the intact protein
scaffold, is a single chromosme. However, this DNA is not straight.
Instead, it is wound around proteins, and the coils are then coiled.
Humans generally have 42 pairs of chromosomes.
Thus, in a sense, a chromosome is like a single volume of an
encyclopedia. The ink used to print each article is DNA. Each
article is a gene. Page numbers and section headings are the control
sequences while the "meaty bits" of the articles are the protein
templates. The articles are printed on paper. The paper is the
protein scaffolding. The entire encyclopedia is a genome. Of course,
the ink in an encyclopedia is not one long strand of ink, but the
analogy is still useful.
Another way to visualize it would be to take an enormous number of
multicolored pipecleaners. String together some white ones for a
promoter. Use a red one as a 5'-UTR. Use a green one (or more) as an
exon. Insert a white one or two or three (or more) as an intron.
Repeat exons and introns for a while, 3-10 of them. Use a blue one as
a 3'-UTR and a yellow one or two or more as a terminator. Now, make a
whole bunch of those things, with different numbers of exons and
introns and different lengths. Now string them all together. Once in
a while, insert a purple one or two. In roughly the middle of the big
string, have several purple ones. Coil the strand up nice and tight,
and build a scaffold out of wood or cardboard. Glue the purple
pipecleaners that are exposed to the scaffold. You've built a model
of a chromosome that's worthy of a college lecture.

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